We can test and validate the convergence and accuracies of these approximations as follows.
On the one hand, as in the DGM and PINN methods, see [1]} and [2]}, we can compute the losss \({\mathcal {L}}_{res}\)  and \({\mathcal {L}}_{term}\) , associated respectively to the residual and to the terminal condition of the partial differential equation (REF )
\( \begin{split}  {\mathcal {L}}_{res} := \frac{1}{|{\mathcal {T}}||\chi |} \sum _{t\in {\mathcal {T}}, x\in \chi } \Big | \partial _t \vartheta ^\eta + H(x,D_x \vartheta ^\eta , D_x ^2 \vartheta ^\eta ) \Big |^2,\end{split} \) 
\( \begin{split}  {\mathcal {L}}_{term} := \frac{1}{|\chi |} \sum _{x\in \chi } \Big | \vartheta ^\eta (T,x) - g(x) \Big |^2,\end{split} \) 
